Ed Thorp
Mathematician and author of Beat the Dealer
Born 1932
Applied probability theory first to blackjack and then to markets, and helped popularise mathematical thinking about bet sizing and risk.
Biography
Edward Thorp, born in Chicago in 1932, is an American mathematician who applied probability first to casino games and then to financial markets. He completed a doctorate in mathematics at UCLA in 1958 and taught at the Massachusetts Institute of Technology, New Mexico State University and the University of California, Irvine, where he spent most of his academic career.
His first public result was in blackjack. Using an IBM 704, he worked out that the odds in the game shift as cards leave the deck, and that a player tracking what has already been dealt can identify the moments when the remaining cards favour them. He tested the system in Nevada casinos in 1961 and published Beat the Dealer the following year. With Claude Shannon he also built a small wearable computer to predict where a roulette ball would settle, generally described as the first device of its kind.
He then applied the same procedure to securities. Beat the Market, written in 1967 with Sheen Kassouf, showed that warrants were systematically mispriced relative to the shares they converted into, and that holding the warrant against an offsetting position in the stock could capture the difference while removing most of the exposure to the market. He was pricing and hedging convertible securities on this basis before the option pricing formula that later made the technique standard was published in 1973.
In 1969 he co-founded Princeton/Newport Partners, running its Newport Beach office while Jay Regan ran the Princeton one. The firm closed at the end of the 1980s after a federal investigation into the Princeton office; Thorp was not charged, and the convictions that followed were overturned on appeal in 1991. He later ran Ridgeline Partners, a statistical arbitrage fund, from 1994 until 2002. In 1991 a client asked him to review Bernard Madoff's reported results, and he concluded they could not be genuine, seventeen years before the fraud collapsed.
Career timeline
- 1932Born in Chicago, Illinois.
- 1958Completes a doctorate in mathematics at the University of California, Los Angeles.
- 1961Tests a wearable computer built with Claude Shannon to predict roulette, and tests card counting in Nevada casinos.
- 1962Publishes Beat the Dealer, setting out a card-counting system for blackjack.
- 1967Publishes Beat the Market with Sheen Kassouf, on hedging mispriced warrants.
- 1969Co-founds Princeton/Newport Partners and runs its Newport Beach office.
- 1991Reviews Bernard Madoff's reported results for a client and concludes they cannot be real.
- 1994Launches Ridgeline Partners, a statistical arbitrage fund, which runs until 2002.
- 2017Publishes A Man for All Markets, his account of the whole sequence.
Investment philosophy
He looks for a measurable edge and refuses to act without one. Card counting, warrant hedging and statistical arbitrage are the same procedure applied to different material: find a situation where the odds can actually be calculated, verify the calculation against reality, act while the edge holds, and stop when it closes. Everything else is opinion, and opinion is not something he is willing to stake money on.
Sizing is the other half of the problem, and the half most people skip. The Kelly criterion gives a mathematical answer to how much of a bankroll to stake given the size of the edge and the odds on offer. Stake too much and an ordinary run of bad luck ends the game while the edge is still real, which is why survival comes before maximisation in everything he has written about position sizing.
Verify before you trust. He tested blackjack in real casinos rather than only on paper, tested the roulette device before relying on it, and applied the same scepticism to a fund whose reported results were far too smooth to have come from actual markets. The habit is consistent: a claim about the world is worth exactly as much as the check you have run on it.
Key ideas
Tap any idea to expand a plain-English explanation, why it matters, and where to learn more.
Look for a measurable edge
The insistence on acting only where the odds can be calculated and verified, rather than where a situation merely looks attractive.
It draws a hard line between analysis and hope, and it explains why he sat out anything he could not quantify rather than settling for a plausible story.
In blackjack the edge appears only in specific deck conditions, so most hands are played at minimum stakes and the money goes on when the count says so.
Position size is half the answer
The Kelly criterion, which sets how much of a bankroll to stake based on the size of the edge and the odds available.
Two people with the same correct view can end up in completely different places depending on how much they put behind it.
An investor with a genuine advantage who stakes far too much on each opportunity can still be wiped out by a normal losing streak.
Hedging removes the bet you did not want
Holding an offsetting position so that a trade captures the specific mispricing you identified without also taking a view on the whole market.
It isolates the thing you actually have an opinion about, which is the only part where the edge exists.
Buying a mispriced convertible security while shorting the underlying share leaves the pricing gap and takes out most of the market exposure.
Surviving beats being right
The principle that a strategy must be able to withstand a bad run, because an edge only pays out to someone still in the game when it does.
Ruin is permanent in a way that a drawdown is not. The arithmetic of recovering from a very large loss is far worse than most people assume.
A position that falls by half needs to double just to get back to where it started, and a position that falls further needs much more than that.
Check the numbers yourself
Running your own arithmetic on a claim rather than accepting a reported figure, particularly when the figure is unusually good.
Fabrications tend to be internally inconsistent, and the inconsistency is often visible from the outside to anyone who bothers to look.
Results that are steadily positive month after month, through conditions that hurt everyone else, describe a pattern real markets do not produce.
Major contributions
- Worked out and published a card-counting system for blackjack, which changed how casinos deal and shuffle the game.
- Built, with Claude Shannon, what is generally described as the first wearable computer, to predict the outcome of a roulette wheel.
- Showed that warrants were systematically mispriced and that a hedged position could capture the gap, years before option pricing theory made the idea standard.
- Brought the Kelly criterion into investment practice, establishing position sizing as a mathematical question rather than a matter of nerve.
- Demonstrated that a fund could be run on quantitative methods alone, which helped make the whole category respectable.
Major successes
- Published Beat the Dealer in 1962, which put a workable card-counting system into general circulation for the first time.
- Co-built the wearable computer with Claude Shannon that is generally credited as the first of its kind.
- Priced and hedged convertible securities systematically before the formula that later made the practice routine had been published.
- Ran Princeton/Newport Partners from 1969 and later Ridgeline Partners, both built on quantitative methods rather than on judgment about individual companies.
- Reviewed Bernard Madoff's reported results in 1991 and told the client who had asked that they could not be genuine.
Important books
- Beat the Dealer1962
The blackjack book, and the one that made his name outside mathematics. Its argument is that the odds in the game change as cards are dealt, and that the change is trackable.
- Beat the Market1967
Written with Sheen Kassouf. Sets out the warrant hedging approach that carried the same reasoning from casino games into securities.
- The Mathematics of Gambling1984
A collection covering the probability behind several games, and the clearest short statement of how he thinks about odds and stakes.
- A Man for All Markets2017
His memoir, and the accessible account of the whole sequence from blackjack tables to hedge funds, including the Madoff episode.
Influence on investors
Thorp is the direct ancestor of quantitative investing as a working practice rather than as a theory. The pattern he established, of finding a statistically identifiable edge, hedging away everything that is not the edge, and sizing positions by arithmetic instead of conviction, is the template that the quantitative funds of the following decades were built on.
His second and broader influence is on how ordinary investors think about position sizing. Before him, how much to put into an idea was treated as a matter of temperament. The Kelly framework made it a calculation with a right answer given your assumptions, and even investors who never run the formula now accept that the size of a position is a decision in its own right rather than a by-product of enthusiasm.
Criticisms and debates
A balanced view includes the main criticisms and open debates, presented neutrally.
- The Kelly criterion is aggressive. Paul Samuelson argued against it over many years on the grounds that maximising the growth rate of wealth is not what most people actually want, and that it exposes them to swings they cannot live through. Practitioners commonly stake a fraction of the Kelly amount for exactly this reason.
- The whole approach depends on having a genuine, measurable edge. Most investors do not have one, and applying precise sizing rules to an imagined advantage makes the outcome worse rather than better.
- The gambling frame travels badly. A blackjack shoe has known odds that repeat under stable rules; a market does not, and treating an investment as a repeated bet with calculable probabilities imports a certainty that is not there.
- Hedge fund records from that era were reported by the manager and are hard to verify independently, so the historical results are not comparable with an audited public benchmark.
- Princeton/Newport closed at the end of the 1980s after a federal investigation into its Princeton office. Thorp, who ran the separate Newport Beach office, was not charged, and the convictions were overturned on appeal in 1991, but the episode still ended the firm.
Lessons for investors
Plain-English takeaways. Context for learning, not advice to buy or sell anything.
- 1An edge you cannot measure is a hope, and sizing a position around a hope is how accounts get ruined.
- 2How much you stake on an idea matters as much as whether the idea is right.
- 3A strategy has to be survivable, because a bad run can end the game long before the odds get a chance to pay out.
- 4Results that look too steady to be real usually are not, and the arithmetic is often enough to show it from the outside.
Notable quotes
“The amount you bet matters as much as whether you are right.”
Context: Thorp was writing about position sizing, worked out mathematically across many repeated bets. The betting frame belongs to that setting.
“I learned that being right is not enough; you have to be right and survive.”
Frequently asked questions
Who is Ed Thorp?
Ed Thorp is an American mathematician born in 1932 who applied probability theory first to blackjack and then to financial markets. He wrote Beat the Dealer and Beat the Market, and ran two quantitative investment funds.
What is card counting?
It is tracking which cards have already been dealt in blackjack, because the odds shift as the composition of the remaining deck changes. When the remaining cards favour the player, the player raises their stake.
What is the Kelly criterion?
It is a formula for how much of a bankroll to stake on an opportunity, based on the size of your edge and the odds on offer. It maximises the long-run growth rate of wealth, at the cost of accepting large swings along the way.
How did Thorp apply gambling mathematics to markets?
He looked for securities whose prices were inconsistent with each other rather than for companies he liked. Warrants trading out of line with the shares they converted into gave a calculable edge that could be hedged and sized like a bet with known odds.
Is the Kelly criterion suitable for an individual investor?
It assumes you can measure your edge, which most individuals cannot, and full Kelly sizing produces swings that few people tolerate. Practitioners who use it typically stake a fraction of the amount it suggests.
What happened to Princeton/Newport Partners?
The firm closed at the end of the 1980s following a federal investigation into its Princeton office. Thorp ran the separate Newport Beach office and was not charged, and the convictions that followed were overturned on appeal in 1991.
How did Thorp identify the Madoff fraud?
A client asked him to examine the reported results in 1991. The returns were far too smooth and too consistent to have come from the strategy described, and individual trades on the statements did not match the market records for those days, so he reported that the results could not be real.
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